LHR-5:30am OK for 7:30 UA flight to USA?

Heathrow is a huge airport and the only one where my rule of thumb is to arrive 3 hours early. But so early in the day, I believe you will be OK, especially if not checking baggage. Recommend you check in online to avoid the counters and kiosks altogether.

I read that when traveling back to USA one still has to go to counter to have documents checked.

Elaine, My experience is British Airways, but we just show our documents at the desk at the gate. Takes 2 seconds.

I have had the flights that early, I don't remember if we left to be there 3 hours early but I know we were standing in line in a dark ghostly terminal. I would try to be there about 1/2 before the desk opens if you are checking luggage. If you are staying near the airport it shouldn't be a big deal, if you have to fight traffic, remember everyone else may be going to work at that time.

Simply, if you can check in online and print out a boarding pass the night before then go at 5:30.
Lately, there is extra screening that will not allow you to check in online when traveling back to the USA.
You will get that specific message when you attempt to checkin online 24 hours in advance.

Or stay out at LHR at Hilton or Sofitel.

05:30 can be a surprisingly busy time at Heathrow primarily boosted from business traffic. However, T2 is still relatively less crowded than the others.

What does UA recommend ?

Yes, you can check in and print a boarding pass for United before going to LHR. But (unless things have changed recently) even with just a carry on you still have to go through their check in counter where your documents are checked and (most times) they will print you a new boarding pass.

2 hours should be OK as long as you are standing at the counter at the 2 hour mark, not getting out of the taxi or train at the 2 hour mark.

United just states you must be checked in including all luggage checked in 90 minutes before your flight departs from LHR. Their check in counter doesn't open until 05:00, so getting there earlier won't do any good

Good luck.

Keep in mind that once you clear security, there is a brisk 15-20 minute walk to the United concourse in terminal 2. It might be worthwhile thinking about arriving at 5 am just in case security takes a little longer.

Have a great trip!

Follow what UA instructs regarding what time to arrive at LHR.

Check in online up to 24 hours early on the UA app. Don't worry about printing your boarding pass. When you check in on the app, load the mobile boarding pass to your smartphone. The mobile boarding pass is available on iPhones, Android, & Windows. Done.